Abstract-In evolutionary multi-objective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms. In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector guided evolutionary algorithm for many-objective optimization. The reference vectors can not only be used to decompose the original multiobjective optimization problem into a number of single-objective sub-problems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front. In the proposed algorithm, a scalarization approach, termed angle penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art evolutionary algorithms for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular Pareto fronts. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.
Abstract-The interests in multi-and many-objective optimization have been rapidly increasing in the evolutionary computation community. However, most studies on multi-and many-objective optimization are limited to small-scale problems, despite the fact that many real-world multi-and many-objective optimization problems may involve a large number of decision variables. As has been evident in the history of evolutionary optimization, the development of evolutionary algorithms for solving a particular type of optimization problems has undergone a co-evolution with the development of test problems. To promote the research on large-scale multi-and many-objective optimization, we propose a set of generic test problems based on design principles widely used in the literature of multi-and many-objective optimization. In order for the test problems to be able to reflect challenges in real-world applications, we consider mixed separability between decision variables and non-uniform correlation between decision variables and objective functions. To assess the proposed test problems, six representative evolutionary multi-and manyobjective evolutionary algorithms are tested on the proposed test problems. Our empirical results indicate that although the compared algorithms exhibit slightly different capabilities in dealing with the challenges in the test problems, none of them are able to efficiently solve these optimization problems, calling for the need for developing new evolutionary algorithms dedicated to large-scale multi-and many-objective optimization.
Evolutionary multi-objective optimization aims to provide a representative subset of the Pareto front to decision makers. In practice, however, decision makers are usually interested in only a particular part of the Pareto front of the multi-objective optimization problem. This is particularly true when the number of objectives becomes large. Over the past decade, preference-based multi-objective optimization has attracted increasing attention from both academia and industry due to its significance in both theory and practice. Significant progress has been made in evolutionary multiobjective optimization and multi-criteria decision communities, although many open issues still remain to be addressed. This paper provides a concise review on preference-based multi-objective optimization, including various preference modeling methods and existing preference-based optimization methods, as well as a brief discussion of the main future challenges.
Abstract. Dynamic optimization using evolutionary algorithms is receiving increasing interests. However, typical test functions for comparing the performance of various dynamic optimization algorithms still lack. This paper suggests a method for constructing dynamic optimization test problems using multi-objective optimization (MOO) concepts. By aggregating different objectives of an MOO problem and changing the weights dynamically, we are able to construct dynamic single objective and multi-objective test problems systematically. The proposed method is computationally efficient, easily tunable and functionally powerful. This is mainly due to the fact that the proposed method associates dynamic optimization with multi-objective optimization and thus the rich MOO test problems can easily be adapted to dynamic optimization test functions.
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